“If these guys are so impressed with themselves, and if they are so sure of their correctness, why doesn't President Obama come on my show? We will do a one-on-one debate of ideas and policies,” Limbaugh said on his radio program Wednesday. “So let's have the debate! I am offering President Obama to come on this program — without staffers, without a TelePrompTer, without note cards — to debate me on the issues.”

POLITICO reported Wednesday on the Democratic effort to portray Limbaugh as the leader of the Republicans, an effort carried out by high-profile Democratic strategists like James Carville and Paul Begala. Top White House officials, including chief of staff Rahm Emanuel, have joined in, and a senior White House aide is helping to guide the Limbaugh strategy, Politico reported.

Limbaugh equated the effort to the “enemies list” once maintained by former President Richard Nixon. “This is being led from the White House. There is an orchestrated attack, daily drumbeat on me from the White House,” Limbaugh said.

“Your flunkies are demanding this debate,” Limbaugh said to Obama. “Your flunkies are targeting a private citizen with an enemies list that so far has three or four names on it: Mine; [CNBC’s] Rick Santelli; Jim Cramer at CNBC; and let's not forget Joe the Plumber, who your allies in Ohio also tried to destroy.”

“The difference is that Joe the Plumber does not have his own microphone every day. They're shutting Santelli up at CNBC. They're going to shut Cramer up pretty soon, too, but he'll go down with a fight,” Limbaugh said. “That isn't going to happen here, to me.”

White House Press Secretary Robert Gibbs conceded Wednesday that engaging media personalities like Limbaugh and Santelli “may be counterproductive.”

“Are there days where I just turn my television off? Yes,” Gibbs said. “There are days when, yeah, you’re head drops from listening to arguments that aren’t necessarily centered on delving into some important issue, but on finding two people on completely opposite ends of the spectrum to yell loudest.”